#include<bits/stdc++.h>
using ll=long long;
#define int ll
template<typename T>using V=std::vector<T>;
using vi=V<int>;
using std::cin,std::cerr,std::cout;
#define all(c) std::begin(c),std::end(c)
#define eb emplace_back
constexpr int K=60;
signed main(){
	cin.tie(0)->sync_with_stdio(0);
	int T;
	cin>>T;
	while(T--){
		int n;
		cin>>n;
		vi fa(n+1);
		V<vi> e(n+1);
		for(int i=2;i<=n;++i){
			cin>>fa[i];
			e[fa[i]].eb(i);
		}
		V<std::multiset<int>>h(n+1);
		int ans=0;
		for(int u=n;u;--u){
			if(empty(e[u])){
				h[u].emplace(0);
			}
			for(int v:e[u]){
				for(int x:h[v])h[u].emplace(x+1);
			}
			while(u==1||h[u].size()>1){
				if(h[u].empty())break;
				int x=*h[u].rbegin();
				h[u].extract(x);
				ans=std::max(ans,x);
			}
		}
		printf("%lld\n",ans);
	}
}